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Computational Optimization and Applications

, Volume 47, Issue 3, pp 455–476 | Cite as

Variable target value relaxed alternating projection method

  • A. Cegielski
  • R. Dylewski
Article

Abstract

In this paper we propose a modification of the von Neumann method of alternating projection x k+1=P A P B x k where A,B are closed and convex subsets of a real Hilbert space ℋ. If Fix P A P B then any sequence generated by the classical method converges weakly to a fixed point of the operator T=P A P B . If the distance δ=inf xA,yB xy is known then one can efficiently apply a modification of the von Neumann method, which has the form x k+1=P A (x k +λ k (P A P B x k x k )) for λ k >0 depending on x k (for details see: Cegielski and Suchocka, SIAM J. Optim. 19:1093–1106, 2008). Our paper contains a generalization of this modification, where we do not suppose that we know the value δ. Instead of δ we apply its approximation which is updated in each iteration.

Keywords

Alternating projection method Relaxation 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.University of Zielona GóraZielona GóraPoland

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